Problem 4.128
[Difficulty: 3]
CS
(moves
at speed U)
y
x
c
d
R
x
R
y
Given:
Water jet striking moving vane
Find:
Force needed to hold vane to speed U = 10 m/s
Solution:
Basic equations: Momentum flux in x and y directions
Assumptions:
1) Steady flow
2) Incompressible flow 3) Atmospheric pressure in jet 4) Uniform flow 5) Jet relative velocity is
constant
Then
R
x
u
1
ρ
−
V
1
⋅
A
1
⋅
()
⋅
u
2
ρ
V
2
⋅
A
2
⋅
⋅
+
=
VU
−
−
ρ
−
⋅
A
⋅
[]
⋅
−
(
) cos
θ
⋅
ρ
−
⋅
A
⋅
⋅
+
=
R
x
ρ
−
2
A
⋅
cos
θ
() 1
−
⋅
=
Using given data
R
x
1000
kg
m
3
⋅
30
10
−
m
s
⋅
⎡
⎣
⎤
⎦
2
×
0.004
×
m
2
⋅
cos 120 deg
⋅
1
−
×
Ns
2
⋅
kg m
⋅
×
=
R
x
2400
−
N
=
Then
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 Fall '07
 Lear
 Fluid Dynamics, Fluid Mechanics, Flux, Velocity, Ry, Jet relative velocity

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